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Convert 32842 from base ten to base eight. I got stuck after I did the place values.

1 Answer

3 votes
The digits of the base 8 representation can be found by checking the remainder upon dividing the original number and the integer parts of its successive quotients by increasing powers of 8.

First digit (from the right):
\frac{32842}8=4105+\frac28\implies2

Second digit:
\frac{4105}8=513+\frac18\implies1

Third digit:
\frac{513}8=64+\frac18\implies1

Fourth digit:
\frac{64}8=8+\frac08\implies0

Since there's no remainder here, move on to the next power of 8:

Fifth digit:
(64)/(8^2)=1+\frac08\implies0

Again, no remainder, so move on to the next power.

Sixth digit:
(64)/(8^3)=\frac18\implies1

Now the base 8 representation will have digits matching the remainders above.


32842_(10)=100112_8
User BaruchLi
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